Chapter 1: Linear and Chapter 1: Linear and Quadratic functions Quadratic functions

By Chris Muffi

1-1 Points and Lines1-1 Points and Lines

Vocabulary-◦Coordinates- ordered pair of numbers◦x-axis- is the horizontal line ◦y-axis- is the vertical line◦Origin- the x and y- axis point of origin◦Quadrants- the axis divides them into 4 of them ◦Solution- is an ordered pair of numbers that

makes the equation true.

1-1 Formulas to know1-1 Formulas to knowMid-Point Formula:

M =

Distance Formula

Ab=

2,

22121 yyxx

212

212 yyxx

1-1 Example1-1 ExampleUse A(4, 2), B(2, 10), C(-2, 9), and D(0,

1).A. Show that and bisect each

other.B. Show that AC = BC.C. What kind of figure is ABCD?D. Find the length of .E. Find the midpoint of .

AC BD

AC

AC

1-2 Slope of lines1-2 Slope of linesSlope

Facts to know◦Horizontal lines have a slope of zero◦Vertical lines have no slope◦Negative slopes fall to the right

12

12

xxyy

runrisem

Slope-intercept formSlope-intercept form

y= mx + b is slope intercept form

1-3 Equations of Lines1-3 Equations of LinesFormulas:

◦ General FormAx + By= C

◦ Slope intercept Form y = mx + B

◦ Point Slope Form

◦ Intercept Formm

xxyy

1

1

1by

ax

1-4 Linear Functions and 1-4 Linear Functions and ModelsModels

Function- describes a dependent relationship between two quantities

Linear functions have the form f(x) = mx + B

DomainDomain

Domain- is the set of values for which the function is defined. You can think of the domain of a function as the set of input values.

RangeRange

The set of output values is called the range of the function.

1-5 Complex Numbers1-5 Complex NumbersCounting Numbers are 1, 2, 3..Rational Numbers are ratios of integers, to

represent fractional parts of quantities. Irrational Numbers are like these 2

ComplexComplexThese numbers are commonly

referred to as imaginary numbers. And look like these 15 and 1

Pattern of ImaginaryPattern of Imaginary 1111111

11111

11111

111

111

1

6

5

4

3

2

i

ii

i

ii

i

i

1-6 Solving Quadratic Equations1-6 Solving Quadratic Equationsquadratic equation- equation that can be

written in the form where a ≠ 0

Roots◦A root, or solution, of a quadratic equation is a

value of the variable that satisfies the equation.

02 cbxax

Completing the SquareCompleting the Square

completing the square- method of transforming a quadratic equation so that one side is a perfect square trinomial

Steps:◦ Step 1: Divide both sides by the coefficient of so that

will have a coefficient of 1.◦ Step 2: Subtract the constant term from both sides.◦ Step 3: Complete the square. Add the square of one

half the coefficient of x to both sides.◦ Step 4: Take the square root of both sides and solve for

x.

Quadratic FormulaQuadratic Formulaquadratic formula- derived by

completing the square.

aacbbx

242

1-7 Quadratic Functions1-7 Quadratic Functionsa ≠ 0, is the set of points (x, y) that

satisfies the equation then this graph is a parabola

cbxaxy 2

X and Y- InterceptX and Y- InterceptThe y-intercept of a parabola with

equation is c. If > 0, there are two x-

intercepts.If = 0, there is one x-intercept

(at a point where the parabola and the x-axis are tangent to each other).

If < 0, there are no x-intercepts.

cbxaxy 2

acb 42

acb 42

acb 42